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Dynamic Energy Budget theory
1 Basic Concepts 2 Standard DEB model 3 Metabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of compounds 7 Extensions of DEB models 8 Co-variation of par values 9 Living together10 Evolution11 Evaluation
Criteria for general energy models• Quantitative Based on explicit assumptions that together specify all quantitative aspects
to allow for mass and energy balancing
• Consistency Assumptions should be consistent in terms of internal logic, with physics
and chemistry, as well as with empirical patterns
• Simplicity Implied model(s) should be simple (numbers of variables and parameters)
enough to allow testing against data
• Generality The conditions species should fulfill to be captured by the model(s) must be
explicit and make evolutionary sense
• Explanatory The more empirical patterns are explained, the better the model
From Sousa et al 2010Phil. Trans. R. Soc. Lond. B 365: 3413-3428
Empirical special cases of DEB 11.1
year author model year author model1780 Lavoisier multiple regression of heat
against mineral fluxes1950 Emerson cube root growth of bacterial
colonies
1825 Gompertz Survival probability for aging 1951 Huggett & Widdas foetal growth
1889 Arrhenius temperature dependence of physiological rates
1951 Weibull survival probability for aging
1891 Huxley allometric growth of body parts 1955 Best diffusion limitation of uptake
1902 Henri Michaelis--Menten kinetics 1957 Smith embryonic respiration
1905 Blackman bilinear functional response 1959 Leudeking & Piret microbial product formation
1910 Hill Cooperative binding 1959 Holling hyperbolic functional response
1920 Pütter von Bertalanffy growth of individuals
1962 Marr & Pirt maintenance in yields of biomass
1927 Pearl logistic population growth 1973 Droop reserve (cell quota) dynamics
1928 Fisher & Tippitt
Weibull aging 1974 Rahn & Ar water loss in bird eggs
1932 Kleiber respiration scales with body weight3/ 4
1975 Hungate digestion
1932 Mayneord cube root growth of tumours 1977 Beer & Anderson development of salmonid embryos
DEB theory is axiomatic, based on mechanisms not meant to glue empirical models
Since many empirical models turn out to be special cases of DEB theory the data behind these models support DEB theory
This makes DEB theory very well tested against data
Empirical patterns: stylised facts
Feeding During starvation, organisms are able to reproduce, grow and survive for some time At abundant food, the feeding rate is at some maximum, independent of food density
Growth Many species continue to grow after reproduction has started Growth of isomorphic organisms at abundant food is well described by the von Bertalanffy For different constant food levels the inverse von Bertalanffy growth rate increases linearly with ultimate length The von Bertalanffy growth rate of different species decreases almost linearly with the maximum body length Fetuses increase in weight approximately proportional to cubed time
Reproduction Reproduction increases with size intra-specifically, but decreases with size inter-specifically
Respiration Animal eggs and plant seeds initially hardly use O2
The use of O2 increases with decreasing mass in embryos and increases with mass in juveniles and adults The use of O2 scales approximately with body weight raised to a power close to 0.75 Animals show a transient increase in metabolic rate after ingesting food (heat increment of feeding)
Stoichiometry The chemical composition of organisms depends on the nutritional status (starved vs well-fed) The chemical composition of organisms growing at constant food density becomes constant
Energy Dissipating heat is a weighted sum of 3 mass flows: CO2, O2 and N-waste
From Sousa et al 2008Phil. Trans. R. Soc. Lond. B 363:2453 -2464
Empirical patterns 1 11.1a
From Sousa et al 2008Phil. Trans. R. Soc. Lond. B 363:2453 -2464
Empirical patterns 2 11.1b
From Sousa et al 2008Phil. Trans. R. Soc. Lond. B 363:2453 -2464
Topological alternatives 11.1c
From Lika & Kooijman 2011J. Sea Res 66: 381-391
Test of properties 11.1d
From Lika & Kooijman 2011J. Sea Res, 66: 381-391
Applications of DEB theory 11.1e
• bioproduction: agronomy, aquaculture, fisheries• pest control• biotechnology, sewage treatment, biodegradation• (eco)toxicology, pharmacology• medicine: cancer biology, obesity, nutrition biology• global change: biogeochemical climate modeling• conservation biology; biodiversity• economy; sustainable development
Fundamental knowledge
of metabolic organisation
has many practical applications
Innovations by DEB theory 11.1f
• Unifies all life on earth (bacteria, protoctists, fungi/animals, plants)
• Links levels of organisation
• Explains body size scaling relationships
• Deals with energetic and stoichiometric constraints
• Individuals that follow DEB rules can merge smoothly
into a symbiosis that again follows DEB rules
• Method for determining entropy of living biomass
• Biomass composition depends on growth rate
• Product formation has 3 degrees of freedom
• Explains indirect calorimetry
• Explains how yield of biomass depends on growth rate
• Quantitative predictions have many practical applications
DEB theory reveals unexpected links 11.1g
Length, mm
O2
cons
umpt
ion,
μl/h
1/yi
eld,
mm
ol g
luco
se/
mg
cells
1/spec growth rate, 1/h
Daphnia
Streptococcus
respiration length in individual animals & yield growth in pop of prokaryotes have a lot in common, as revealed by DEB theory
Reserve plays an important role in both relationships, but you need DEB theory to see why and how
Weird world at small scale 11.2a
Almost all transformations in cells are enzyme mediatedClassic enzyme kinetics: based on chemical kinetics (industrial enzymes)• diffusion/convection• law of mass action: transformation rate product of conc. of substrates• larger number of molecules• constant reactor volume
Problematic application in cellular metabolism:• definition of concentration (compartments, moving organelles) • transport mechanisms (proteins with address labels, targetting, allocation) • crowding (presence of many macro-molecules that do not partake in transformation)• intrinsic stochasticity due to small numbers of molecules• liquid crystalline properties • surface area - volume relationships: membrane-cytoplasm; polymer-liquid• connectivity (many metabolites are energy substrate & building block; dilution by growth)
Alternative approach: reconstruction of transformation kinetics on the basis of cellular input/output kinetics
Diffusion cannot occur in cells 11.2b
Self-ionization of water in cells 11.2c
A cell of volume 0.25 mm3
and pH 7 at 25°C hasm = 14 protons N = 8 109 water molecules
confidence intervals of pH 95, 90, 80, 60 %
pH
cell volume, m3
modified Bessel function
7
Crowding affects transport 11.2d
cytoskeletal polymers
ribosomes
nucleic acids
proteins
ATP generation & use 11.2e
5 106 ATP molecules in bacterial cell enough for 2 s of biosynthetic work
Only used if energy generating & energy demanding transformations are at different site/time
If ADP/ATP ratio varies, then rates of generation & use varies, but not necessarily the rates of transformations they drive
Processes that are not much faster than cell cycle, should be linked to large slow pools of metabolites, not to small fast pools
DEB theory uses reserve as large slow pool for driving metabolism
Classic energetics 11.3
Anabolism: synthetic pathwaysCatabolism: degradation pathwaysDuality: compounds as source for energy and building blocksIn DEB: from food to reserve; from reserve to structure
From: Mader, S. S. 1993 Biology, WCB
This decomposition occursat several places in DEBs
Classic energetics 11.3a
From: Duve, C. de 1984 A guided tour of the living cell, Sci. Am. Lib., New York
heterotroph autotroph
The classic concept on metabolic regulation focusses on ATP generation and use.The application of this concept in DEB theory is problematic.
Static Energy Budgets 11.3b
From: Brafield, A. E. and Llewellyn, M. J. 1982 Animal energetics, Blackie, Glasgow
C energy from foodP production (growth)F energy in faecesU energy in urineR heat
Numbers: kJ in 28 d
Basic difference with dynamic budgets:Production is quantified as energy fixed in new tissue, not as energy allocated to growth: excludes overheadsHeat includes overheads of growth, reproduction and other processes, it does not quantify maintenance costs
Static vs Dynamic Budgets 11.4
Net production models• time-dependent static models• no demping by reserve
Assimilation models• dynamics by nature• reserve damps food fluctuations
Static Energy Budgets (SEBs) 11.4a
Differences with DEBs• overheads interpretation of respiration interpretation of urination• metabolic memory• life cycle perspective change in states
gross ingested
faeces
urine
apparent assimilated
gross metabolised
net metabolised
spec dynamic action
workmaintenance
somaticmaintenance
activity
thermo regulation
production
growth productsreproduction
Production model 11.4c
food faecesassimilation
feeding defecation
maintenance
offspring
reproductionreserve
structurestructure
growth
Production models 11.4d
• no accommodation for embryonic stage; require additional state variables (no food intake, still maintenance costs and growth)
• no metabolic memory, no growth during starvation
• require switches in case of food shortage (reserves allocated to reproduction used for maintenance)
• no natural dynamics for reserve; descriptive rules for growth vs reprod.
• no explanation for body size scaling of metabolic rates, changes in composition of biomass, metabolic memory
• require complex regulation modelling for fate of metabolites (ATP vs building blocks; consistency problem with lower levels of org.)
• dividing organisms (with reserve) cannot be included
• typically have descriptive set points for allocation, no mechanisms (weight-for-age rules quantify allocation to reproduction)
Dynamic Energy Budget theory
1 Basic Concepts 2 Standard DEB model 3 Metabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of compounds 7 Extensions of DEB models 8 Co-variation of par values 9 Living together10 Evolution11 Evaluation
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